Transrectal electrical impedance tomography (TREIT) has been proposed as an adjunct modality for enhancing standard clinical ultrasound (US) imaging of the prostate. The proposed TREIT probe has an array of electrodes adhered to the surface of a cylindrical US probe that is introduced inside of the imaging volume. Reconstructing TREIT images in the open-domain geometry established with this technique poses additional challenges to those encountered with closed-domain geometries, present in more conventional EIT systems, because of the rapidly decaying current densities at increasing distances from the probe surface. We developed a finite element method (FEM)-based dual-mesh reconstruction algorithm which employs an interpolation scheme for linking a fine forward mesh with a coarse grid of pixels, used for conductivity estimation. Simulation studies using the developed algorithm demonstrate the feasibility of imaging moderately contrasting inclusions at distances of three times the probe radius from the probe surface and at multiple angles about the probe's axis. The large, dense FEM meshes used here require significant computational effort. We have optimized our reconstruction algorithm with multi-core processing hardware and efficient parallelized computational software packages to achieve a speedup of 9.3 times when compared to a more traditional Matlab-based, single CPU solution. The simulation findings and computational optimization provide a state-of-the-art reconstruction platform for use in further evaluating transrectal electrical impedance tomography.